Problem: Solve for $x$ and $y$ using elimination. ${-4x+2y = -26}$ ${3x-2y = 19}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-4x+2y = -26}\thinspace$ to find $y$ ${-4}{(7)}{ + 2y = -26}$ $-28+2y = -26$ $-28{+28} + 2y = -26{+28}$ $2y = 2$ $\dfrac{2y}{{2}} = \dfrac{2}{{2}}$ ${y = 1}$ You can also plug ${x = 7}$ into $\thinspace {3x-2y = 19}\thinspace$ and get the same answer for $y$ : ${3}{(7)}{ - 2y = 19}$ ${y = 1}$